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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Aestimo Tutorial #3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this tutorial, we will look at modelling a structure with a parabolic potential rather than the stepped potentials that aestimo usually considers. In order to do this, we will need to understand how aestimo's code is structured in more depth.\n",
      "\n",
      "This example is a replication of that given in Harrison's book[1] in Ch.3 sec.5.\n",
      "\n",
      "First, we import the libraries that we need as usual."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import aestimo.aestimo as solver\n",
      "import aestimo.config as ac\n",
      "ac.messagesoff = True # turn off logging in order to keep notebook from being flooded with messages.\n",
      "import aestimo.database as adatabase\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import copy\n",
      "from pprint import pprint"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then, we redefine some of the database entries since Harrison's initial examples don't take account of different effective masses in the different materials."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "meV2J = solver.meV2J # conversion factor\n",
      "q = solver.q # electron charge\n",
      "\n",
      "adatabase.materialproperty = {\n",
      "    'GaAs':{\n",
      "        'm_e':0.067,\n",
      "        'm_e_alpha':0.0,\n",
      "        'epsilonStatic':12.90,\n",
      "        'Eg':0.0, #1.426, # set the energy scale origin to be at the GaAs condution band\n",
      "        'Band_offset':0.67,\n",
      "        },\n",
      "    'AlAs':{\n",
      "        'm_e':0.067, # normally Harrison would be using 0.15\n",
      "        'm_e_alpha':0.0,\n",
      "        'epsilonStatic':10.06,\n",
      "        'Eg':2.673-1.426, #2.673, # set the energy scale origin to be at the GaAs condution band\n",
      "        'Band_offset':0.67,\n",
      "        },\n",
      "    }\n",
      "\n",
      "adatabase.alloyproperty = {\n",
      "    'AlGaAs':{\n",
      "        'Bowing_param':0.0,\n",
      "        'Band_offset':0.67,\n",
      "        'Material1':'AlAs',\n",
      "        'Material2':'GaAs',\n",
      "        'm_e_alpha':0.0,\n",
      "        },\n",
      "    }"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we define the system's properties. However, we can't create our 'Structure' object in the usual way using the `StructureFrom` class, instead we will work directly with its parent class `Structure`. We willh ave to create some of the structure object's attributes ourselves, specifically the arrays that describe the system w.r.t. position.\n",
      "\n",
      "The Structure class is used by Aestimo to hold all of the details about the system that is being modelled. In essence, it is a collection of attributes hanging off a class instance plus a method for calculating the effective mass (array) with respect to energy for those times that we ask non-parabolicity to be included in the simulation. These attributes are either scalars or they are 1d arrays of parameters w.r.t. position across the structure. \n",
      "\n",
      "We normally use the subclass `StructureFrom` instead of the `Structure` class since `StructureFrom` knows how to turn the input files into a `Structure` object.The `StructureFrom` class uses the method `create_structure_arrays()` to calculate the attribute arrays from the `material` list structure that we normally use in our input files. So we also need to run this method if we ever update any of the model's parameters during a simulation so that the `Structure` object's arrays are up to date.\n",
      "\n",
      "First, here are the parameters that `StructureFrom` needs:\n",
      "\n",
      "* inputfile object\n",
      "  + material - list of layers describing structure. Each layer is a list of \n",
      "   [Thickness (nm) | Material | Alloy fraction | Doping(cm^-3) | n or p type ]\n",
      "  + T - (float) Temperature (K)\n",
      "  + gridfactor - grid step size (m)\n",
      "  + computation_scheme - (int) computing scheme - see example files for details.\n",
      "  + meff_method - chooses effective mass energy dependent function for times that nonparabolicity is included in simulation - see example files for details. (not needed for the aestimo_h solver\n",
      "  + fermi_np_scheme - (bool) chooses whether to calculate fermi-level including non-parabolicity terms to in-plane dispersion (not needed for the aestimo_h solver)\n",
      "  + subnumber_e - number of subbands to look for.\n",
      "  + subnumber_h - number of valence subbands to look for. (only needed for aestimo_numpy_h solver)\n",
      "  + Fapplied - applied field (Vm**-1)\n",
      "  + maxgridpoints - maximum number of grid points allowed (used only to prevent simulation of structures that are accidentally too large)\n",
      "\n",
      "* database object/module - we give the reference explicitly in case we want to supply a customised object. \n",
      "   This works because modules, classes and namedtuples can often substitute for each other in python.\n",
      "\n",
      "However, if we want to create our own version of the Structure object for aestimo to use, we will need to define\n",
      "\n",
      "#### Custom Structure Class\n",
      "+ **value attributes**\n",
      "  + T - Temperature (K)\n",
      "  + dx - grid step size (m) (gridfactor in input files)\n",
      "  + comp_scheme - (int) computing scheme\n",
      "  + meff_method - (int) effective mass function (see above) (only aestimo not aestimo_h)\n",
      "  + fermi_np_scheme - (bool) (see above) (only aestimo not aestimo_h)\n",
      "  + subnumber_e - number of subbands to look for.\n",
      "  + subnumber_h - number of valence bands (only aestimo_numpy_h)\n",
      "  + Fapp - applied field (Vm**-1) (Fapplied in input files)\n",
      "  + n_max - number of grid points\n",
      "  + x_max - total thickness of structure (m) (currently optional)\n",
      "\n",
      "+ **array attributes**\n",
      "  + fi - Bandstructure potential (J) (array, len n_max)\n",
      "  + eps - dielectric constant (including eps0) (array, len n_max)\n",
      "  + dop - doping distribution (m**-3) (array, len n_max)\n",
      "  + cb_meff - conduction band effective mass (kg) (array, len n_max)\n",
      "\n",
      "+ **method attributes**\n",
      "  + cb_meff_E(E,fi) - given the energy and the effective potential array, returns an array for the effective mass.\n",
      "\n",
      "+ **array attributes 2** (non-parabolicity) - These attributes are only necessary if you are using a non-parabolic model for the effective mass of conduction band elections.\n",
      "  + cb_meff_alpha - non-parabolicity constant. Used for Nelson's empirical 2-band model[2])\n",
      "  + Eg - band gap energy (Used for k.p model found in Vurgaftman[3])\n",
      "  + Ep - (Used for k.p model found in Vurgaftman[3])\n",
      "  + F  - (Used for k.p model found in Vurgaftman[3])\n",
      "  + delta_S0 - spin split-off energy (Used for k.p model found in Vurgaftman[3])\n",
      "\n",
      "+ **array attributes 3** (valence band modelling) - In aestimo_numpy_h there are many more arrays that should be defined but I will not discuss this any further since things are getting complicated enough."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s0 = {} # this will be our datastructure\n",
      "\n",
      "# TEMPERATURE\n",
      "s0['T'] = 300.0 #Kelvin\n",
      "\n",
      "# COMPUTATIONAL SCHEME\n",
      "# 0: Schrodinger\n",
      "# 1: Schrodinger + nonparabolicity\n",
      "# 2: Schrodinger-Poisson\n",
      "# 3: Schrodinger-Poisson with nonparabolicity\n",
      "# 4: Schrodinger-Exchange interaction\n",
      "# 5: Schrodinger-Poisson + Exchange interaction\n",
      "# 6: Schrodinger-Poisson + Exchange interaction with nonparabolicity\n",
      "s0['comp_scheme'] = 0\n",
      "\n",
      "# Non-parabolic effective mass function\n",
      "# 0: no energy dependence\n",
      "# 1: Nelson's effective 2-band model\n",
      "# 2: k.p model from Vurgaftman's 2001 paper\n",
      "s0['meff_method'] = 0 \n",
      "\n",
      "# Non-parabolic Dispersion Calculations for Fermi-Dirac\n",
      "s0['fermi_np_scheme'] = True\n",
      "\n",
      "# QUANTUM\n",
      "# Total subband number to be calculated for electrons\n",
      "s0['subnumber_e'] = 10\n",
      "\n",
      "# APPLIED ELECTRIC FIELD\n",
      "s0['Fapp'] = 0.00 # (V/m)\n",
      "\n",
      "# GRID\n",
      "# For 1D, z-axis is choosen\n",
      "gridfactor= 0.01 #nm\n",
      "s0['dx'] = gridfactor*1e-9\n",
      "maxgridpoints = 200000 #for controlling the size\n",
      "\n",
      "# STRUCTURE\n",
      "# a finite parabolic well between two barriers\n",
      "a = 10.0 #nm #maximum width of parabolic well (at the barrier's energy level)\n",
      "b = 10.0 #nm #width of the first barrier layer\n",
      "b2 = 5.0 #nm #width of the first barrier layer\n",
      "xmin = 0.0 #minimum Al alloy in structure\n",
      "xmax = 10.0 #maximum Al alloy in structure\n",
      "\n",
      "def alloy_profile(z):\n",
      "    \"\"\"function of alloy profile for finite parabolic well\"\"\"\n",
      "    well = xmin + (z - (b+a/2.0))**2 / (a/2.0)**2 * (xmax - xmin)    \n",
      "    return np.where(well<xmax,well,xmax) #cuts off parabolic well at barrier height\n",
      "\n",
      "def bandstructure_profile(x):\n",
      "    mat1 = adatabase.materialproperty['AlAs']\n",
      "    mat2 = adatabase.materialproperty['GaAs']\n",
      "    alloy = adatabase.alloyproperty['AlGaAs']\n",
      "    return alloy['Band_offset']*(x*mat1['Eg'] + (1-x)* mat2['Eg']-alloy['Bowing_param']*x*(1-x))*solver.q # for electron. Joule\n",
      "    #return alloy['Band_offset']*(x*mat1['Eg'] + (1-x)* mat2['Eg'])*aestimo.q # for electron. Joule\n",
      "\n",
      "# Nb. we could have avoided using the database module at all since we are \n",
      "# defining our own Structure object and calculating its attribute arrays \n",
      "# ourselves but I wanted to show how easy it is to customise the database's values.\n",
      "\n",
      "## Create structure arrays -----------------------------------------------------\n",
      "\n",
      "# Calculate the required number of grid points\n",
      "s0['x_max'] = sum([b,a,b2])*1e-9 #total thickness (m)\n",
      "s0['n_max'] = n_max = int(s0['x_max']/s0['dx'])\n",
      "# Check on n_max\n",
      "if s0['n_max'] > maxgridpoints:\n",
      "    solver.logger(\" Grid number is exceeding the max number of %d\", maxgridpoints)\n",
      "    exit()\n",
      "#\n",
      "meff = adatabase.materialproperty['GaAs']['m_e']*solver.m_e\n",
      "epsGaAs = adatabase.materialproperty['GaAs']['epsilonStatic']\n",
      "\n",
      "z = np.arange(0.0,s0['x_max'],s0['dx'])*1e9 #nm\n",
      "\n",
      "s0['cb_meff'] = np.ones(n_max)*meff\t#conduction band effective mass\n",
      "s0['cb_meff_alpha'] = np.zeros(n_max)   #non-parabolicity constant.\n",
      "s0['eps'] = np.ones(n_max)*epsGaAs\t#dielectric constant\n",
      "s0['dop'] = np.ones(n_max)*0.0          #doping\n",
      "s0['fi'] = bandstructure_profile(alloy_profile(z))   #Bandstructure potential\n",
      "\n",
      "# Initialise structure class\n",
      "model = solver.Structure(**s0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#config.d_E = 1e-5*meV2J\n",
      "#config.Estate_convergence_test = 3e-10*meV2J\n",
      "result= solver.Poisson_Schrodinger(model)\n",
      "\n",
      "#Plot QW representation\n",
      "%matplotlib inline\n",
      "ac.wavefunction_scalefactor = 5000\n",
      "solver.QWplot(result)#,figno=None)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "calculation time  2.03413 s\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "INFO:aestimo:calculation time  2.03413 s\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Syqpu3rxJgQIFuHTpEjly5HB0OEo5FWMgI7nXlClT2L59O1OnTrV+UMphMpK3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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb008052c>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that (as expected) the parabolic energy levels are equally spaced, at least for the lower levels which are not so sensitive to the finite height of the barrier potentials."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Energies = np.array(result.E_state)\n",
      "Energies[1:] - Energies[:-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([ 871.88179039,  871.87321772,  871.86216698,  871.82993394,\n",
        "        871.66001195,  870.77565   ,  866.77248077,  850.23643253,\n",
        "        773.81362525])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Paul Harrison, *Quantum Wells, Wires and Dots*, 3rd. Ed. (Wiley, 2010).\n",
      "2. D.F. Nelson et al., Phys. Rev. B **35**, 7770 (1987)\n",
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     ]
    }
   ],
   "metadata": {}
  }
 ]
}